Component Manual Hydraulics

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The component manual describes the components of the library. In accordance with the component categories in the library, the manual subdivides itself into several parts: • Component library Hydraulics • Component library Pneumatics • Component library Control, • Component library Mechanics • Component library Thermal Hydraulics • Component library Modules • Component library Miscellaneous The HYDRAULICs part contains all hydraulic components of the library. This includes pumps and motors, flow valves, pressure valves, check valves, and directional valves as well as accumulators and pipes.

Transcript of Component Manual Hydraulics

  • Component Manual Hydraulics

  • DSHplus

    Copyright 1995-2008 by

    FLUIDON Gesellschaft fr Fluidtechnik mbH

    Jlicher Strae 336

    52070 Aachen

    Germany

    Tel. +49 (0) 241 - 9 60 92 60

    Fax +49 (0) 241 - 9 60 92 62

    www.fluidon.com

    e-mail [email protected]

    No part of the manuals may be reproduced, duplicated or distrib-

    uted in any form (printing, photo print etc.) without permission of

    the FLUIDON GmbH.

    The soft and hardware names mentioned in this manual are in the

    most cases registered trademarks and are subject to the legal de-

    termination as such ones.

    In the course of further development of the software, parts of this

    manual can lose their validity.

  • Introduction

    2008 FLUIDON GmbH III

    Introduction

    The component manual describes the components of the library. In accordance with the

    component categories in the library, the manual subdivides itself into several parts:

    Component library Hydraulics

    Component library Pneumatics

    Component library Control,

    Component library Mechanics

    Component library Thermal Hydraulics

    Component library Modules

    Component library Miscellaneous

    The HYDRAULICs part contains all hydraulic components of the library. This includes pumps

    and motors, flow valves, pressure valves, check valves, and directional valves as well as

    accumulators and pipes.

    The PNEUMATICS part of the library includes many components for pneumatic systems. The

    components range from cylinders and resistors to directional valves and sensors.

    In the manual part MECHANICS the mechanical components are described. These are the

    masses and the spring damper components as well as other mechanical components.

    The component library of DSHplus includes analog and digital components for control

    tasks that are explained in the chapter CONTROL.

    The THERMAL HYDRAULICS part contains thermal hydraulic components of the library. This

    includes pumps and motors and directional valves as well as accumulators and pipes.

    The component manual should help to select the right component for a model and to pa-

    rameterize it. Furthermore, there is information about the kind of modeling of the compo-

    nents, e. g. whether they were modeled in accordance with the physical qualities of the

    real components or whether only their dynamic characteristics were taken.

    The MODULES contains the components for the DSHplus-STC and for the sub model pre-

    pare. The part MISCELLANEOUS contains other components to which the nodes in particular

    belong.

    All components are described according to the same scheme. The following page shows

    an example component with which the scheme is explained.

  • Introduction

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    ComponentName

    Symbol of the component

    Symbol

    Sketch

    Drawing of the component

    Connectors and Variables

    Name Type Unit Description

    Hydraulic connector Hydr Unit short description

    Hydraulic volume less con-

    nector

    Hvol Unit short description

    Thermal hydraulic connec-

    tor

    THydr Unit short description

    Pneumatic connector Pneu Unit short description

    Signal input In short description

    Signal output Out short description

    Mechanical connector Mech short description

    Internal variable V short description

    Parameters

    Name Value Unit Description

    Parameter name Value Unit short description

    Notes

    Remarks about function and application

  • Introduction

    2008 FLUIDON GmbH V

    Comments to the example component:

    The component symbol is the symbol with which a component appears in the li-

    brary and in the model.

    The component with its parameters and its connectors is represented in the com-

    ponent drawing according to the following figure:

    SignalOutput MechanicConnector SignalInput

    HydraulicConnector

    Parameter

    Pneumatic Connector Thermalhydraulic

    Connector

    The arrows at the component specify whether the connector is an input, an output

    or a mechanical connection. The direction of state variables is defined by a coordi-

    nate system.

    In the table Connectors and Variables, all connectors and variables of a compo-

    nent are listed.

    The connectors and variables of a component can be subdivided into different ty-

    pes. They are characterized in the column Type in accordance with:

    Hydr: hydraulic connector

    Pneu: pneumatic connector

    Thydr: thermal hydraulic connector

    In: input of a signal

    Out: output of a signal

    Mech: mechanical connector

    V: internal variable (state variable)

    Units (column Unit) were assigned to the variables. In so far as the customer

    does not change the Units, the graphic or numeric edition of the variables occurs

    with these Units. The units for the values of the other connectors are listed only

    for better understanding.

    In the parameter list, all parameters are listed with its Values and Units with

    which a component is described.

    The Notes give further remarks to the function and the application of the compo-

    nent.

    The following spelling is used:

    COMPONENTNAME

    Parameters, Connectors and Variables

  • Introduction

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  • Hydraulics

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    Contents

    Pumps .................................................................................................................3 Pump................................................................................................................3 VariablePump.....................................................................................................5 PumpRotationalSpeed .........................................................................................7 PumpRotationalSpeedMech..................................................................................9 VariablePumpRotationalSpeed............................................................................ 11 VariablePumpRotationalSpeedMech .................................................................... 13 PressureControlledPump.................................................................................... 15 VariablePressureControlledPump ........................................................................ 17 PumpCharacteristic........................................................................................... 19 VariablePumpCharacteristic ............................................................................... 20 PistonPump ..................................................................................................... 22 VariablePistonPump .......................................................................................... 23

    Motors ............................................................................................................... 25 Rotational Motors ............................................................................................. 25 Linear Motors................................................................................................... 36

    Directional Valves ............................................................................................... 49 2-x Valves ....................................................................................................... 49 3-x Valves ....................................................................................................... 85 4-x Valves ..................................................................................................... 123 Additional valves ............................................................................................ 175

    Resistors.......................................................................................................... 196 Orifice........................................................................................................... 196 OrificeVarCDType1 ......................................................................................... 198 OrificeVarCDType2 ......................................................................................... 200 VariableOrifice ............................................................................................... 203 Nozzle........................................................................................................... 205 VariableNozzle ............................................................................................... 207 MeeteringEdge ............................................................................................... 209 OrificeyACharacteristic .................................................................................... 211 Throttle......................................................................................................... 213 VariableThrottle ............................................................................................. 215 Bore ............................................................................................................. 217 VariableBore .................................................................................................. 219 Gap .............................................................................................................. 221 VariableGap................................................................................................... 223 TechnResistor ................................................................................................ 225 VariableTechResistor....................................................................................... 227 ThrottleCheckValve......................................................................................... 229 ResistorpQCharacteristic ................................................................................. 230 ResistorpQyCharacteristic................................................................................ 232

    Flow Valves ...................................................................................................... 234 StaticFlowController........................................................................................ 234 StaticFlowControllerVariable ............................................................................ 236 FlowControllerDownstreamOfCompensator ........................................................ 238 VariableFlowControllerDownstreamOfCompensator ............................................. 241 FlowControllerUpstreamOfCompensator ............................................................ 244 VariableFlowControllerUpstreamOfCompensator ................................................. 247 StaticThreeWayFlowController.......................................................................... 250 StaticThreeWayFlowControllerVariable .............................................................. 252 ThreeWayFlowController.................................................................................. 254 ThreeWayFlowControllerVariable ...................................................................... 257 FlowDivider ................................................................................................... 260

    Pressure Valves ................................................................................................ 262

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    PLVstatic ....................................................................................................... 262 AdjustPLVstatic .............................................................................................. 264 PLVdirect....................................................................................................... 266 AdjustPLVdirect .............................................................................................. 268 PLVpiloted ..................................................................................................... 270 PRVstatic....................................................................................................... 274 VariablePRVstatic ........................................................................................... 275 PRVdirect ...................................................................................................... 277 PCVstatic....................................................................................................... 279 ProportionalPressureControlValve ..................................................................... 281

    Check Valves .................................................................................................... 283 CheckValve.................................................................................................... 283 CheckValvePT1............................................................................................... 285 CheckValvedirect ............................................................................................ 287 PilotControlledCheckValve ............................................................................... 290 PilotControlledCheckValveDynamic ................................................................... 293 ChangeoverValve............................................................................................ 296

    Accumulators.................................................................................................... 297 BladderAccumulator........................................................................................ 297 PistonAccumulator .......................................................................................... 300 PistonAccumulatorPneu ................................................................................... 303 PistonGasAccumulator..................................................................................... 305 DiaphragmSpringAccumulator .......................................................................... 307 AccumulatorpVCharacteristic............................................................................ 308 BladderAccumulatorPneu ................................................................................. 309

    Pipes & Reservoirs............................................................................................. 312 Automotive Lines............................................................................................ 312 PipeConcParam .............................................................................................. 359 PipeConcParam5fold ....................................................................................... 361 PipeConcParam10fold...................................................................................... 363 PipeWithFriction ............................................................................................. 366 HoseConcParam ............................................................................................. 368 Reservoir....................................................................................................... 371 PipeDistributedParam...................................................................................... 373 PipeEnd......................................................................................................... 375 PipeEndResistance.......................................................................................... 376 PipeEndQIn.................................................................................................... 378 PipeConnection .............................................................................................. 379 PipeResistance ............................................................................................... 380 Elbow............................................................................................................ 381

    Miscellaneous ................................................................................................... 383

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    Hydraulics

    Pumps

    Pump

    Symbol

    Sketch

    pP

    pT

    InternalLeakage

    ExternalLeakage

    ExternalLeakage

    Connectors and Variables

    Name Type Unit Description

    pP Hydr bar working pressure

    pT Hydr bar reservoir pressure

    VolumeFlow Out l/min delivery

    Parameters

    Name Value Unit Description

    VolumeFlow 30 l/min flow at no leakage

    InternalLeakage 0.01 l/min/bar internal leakage

    ExternalLeakage 0 l/min/bar theoretical pump delivery

    CavitationPressure -0.5 bar Pressure limit at which cavitation

    starts

    Notes

    The component part PUMP constitutes a model of a flow source in which the delivery is calculated from the given nominal flow and the leakage. The leakage is dependent on the adjacent pressure difference pP - pT.

    The VolumeFlow refers to the connection pP.

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    The component part PUMP does not provide a model of the physical design of a pump but only copies its characteristic features. Thus, physical parameters (e.g. inertia moment or hydraulic-mechanical efficiency) are not parameterized.

    A model of an invariable flow source is also available as a component part in which the dependency of flow and adjacent pressure difference is described via a characteristic field (PUMPCHARACTERISTICS).

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    VariablePump

    Symbol

    Sketch

    p1

    p2

    InternalLeakage

    Input

    ExternalLeakage

    ExternalLeakage

    Connectors and Variables

    Name Type Unit Description

    p1 Hyd bar pressure 1

    p2 Hyd bar pressure 2

    VolumeFlow Out l/min Delivery

    Input In - signal for the control of the

    pump displacement

    Parameters

    Name Value Unit Description

    VolumeFlow 30 l/min flow at no leakage and at maxi-

    mum displacement

    InternalLeakage 0.01 l/min/bar internal leakage

    ExternalLeakage 0 l/min/bar theoretical pump delivery

    InputMax 1 - standardization parameter for

    the input signal

    InputMin -1 - standardization parameter for

    the input signal

    CavitationPressure -0.5 bar Pressure limit at which cavitation

    starts

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    Notes

    The component part VARIABLEPUMP constitutes a model of a variable flow source, The deliv-ery is calculated from the parameters VolumeFlow, the input signal and the leakage. The leakage is dependent on the adjacent pressure difference pP - pT.

    Depending on the direction of the rotation, both p1 and p2 can designate the high pres-sure side of the pump. (Irrespective of the delivery direction) The VolumeFlow on princi-ple refers to the connection p1.

    The component part VARIABLEPUMP is no model of the physical design of a pump but only copies its characteristic features. Therefore, physical characteristics (e.g. inertia moment or hydraulic-mechanical efficiency) are not parameterized.

    A model of a variable flow source is also available as a component part in which the de-pendency on the VolumeFlow, input signal, and adjacent pressure difference can be de-scribed via a look-up-table (VARIABLEPUMPCHARACTERISTICS).

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    PumpRotationalSpeed

    Symbol

    Sketch

    pP

    pT

    InternalLeakage

    InertiaMomentViscousDamping

    RotationalSpeedTorque

    DisplacementVolumeEthaHM

    RotationalSpeedTorque

    +

    ExternalLeakage

    ExternalLeakage

    Connectors and Variables

    Name Type Unit Description

    PP Hydr bar working pressure

    PT Hydr bar reservoir pressure

    RotationalSpeed In 1/min input of rotational speed

    VolumeFlow Out l/min delivery

    LoadTorque Out Nm required torque of the drive at

    given rotational speed

    Parameters

    Name Value Unit Description

    DisplacementVolume 32 cm delivery at a rotation of the

    pump without leakage

    ViscousDamping 1 Nms speed-dependent damping

    CavitationPressure -0.5 bar Pressure limit at which cavita-

    tion starts

    InternalLeakage 0.01 l/min/bar internal leakage

    ExternalLeakage 0 l/min/bar theoretical pump delivery

    EthaHM 1 - hydro-mechanical efficiency

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    Name Value Unit Description

    InertiaMoment 0.05 kgm inertia moment of the rotating

    parts of the pump

    DifferentiationTime 1 ms help parameter for calculation of

    the momentum

    PrefixMomentum -1 - prefix of output

    Notes

    The component part PUMPROTATIONALSPEED constitutes a model of a displacement pump in which the RotationalSpeed is predefined and the required Torque of the drive is calcu-lated. Inertia and friction momentum are considered.

    The torque is differentiated from the spin equation. This demands the parameter Differen-tiationTime.

    By means of the parameter PrefixMomentum the prefix of the Torque can be adjusted according to the requirements for the connection to further component parts.

    Depending on the direction of the rotation, both pP and pT can designate the high pres-sure side of the pump. (Irrespective of the delivery direction) The VolumeFlow on princi-ple refers to the connection pP.

    A model of a pump with variable angular velocity is also available as a component part in which the connections for the AngularVelocity and the Torque are united in one mechani-cal connection (PUMPROTATIONALSPEEDMECH).

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    PumpRotationalSpeedMech

    Symbol

    Sketch

    pP

    pT

    InternalLeakage

    InertiaMomentViscousDamping

    MechTorque

    DisplacementVolumeEthaHM

    MechomegaMechM, Torque

    +

    ExternalLeakage

    ExternalLeakage

    Connectors and Variables

    Name Type Unit Description

    pP Hydr bar working pressure

    pT Hydr bar reservoir pressure

    Mech

    Mechomega

    MechM

    Mech

    In

    Out

    -

    deg/s

    Nm

    mechanical connection

    angular velocity

    required torque

    VolumeFlow Out l/min delivery

    Parameters

    Name Value Unit Description

    DisplacementVolume 32 cm displacement volume at a rota-

    tion without leakage

    InertiaMoment 0.05 kgm Inertia moment of working parts

    of the pump

    ViscousDamping 1 Nms speed-dependent damping

    InternalLeakage 0.01 l/min/bar internal leakage

    ExternalLeakage 0 l/min/bar theoretical pump delivery

    CavitationPressure -0.5 bar Pressure limit at which cavita-

    tion starts

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    EthaHM 1 - hydro-mechanical efficiency

    DifferentiationTime 1 ms help parameter for calculation of

    the momentum

    PrefixMomentum -1 - prefix for the output of the mo-

    mentum

    Notes

    The component part PUMPROTATIONALSPEEDMECH constitutes a model of a displacement pump in which the RotationalSpeed is predefined and the required Torque of the drive is calculated. Inertia and friction momentum are considered. The connections for the angu-lar velocity (Mechomega) and the output torque (MechM) are united in the mechanical connection Mech.

    The Torque is differentiated from the spin equation. This demands the parameter Differ-entiationTime.

    By means of the parameter PrefixMomentum the prefix of the Torque can be adjusted according to the requirements for the connection to further component parts.

    Depending on the direction of the rotation, both pP and pT can designate the high pres-sure side of the pump. (Irrespective of the delivery direction) The VolumeFlow on princi-ple refers to the connection pP.

    A model of a pump with variable angular velocity is also available as a component part in which the connections for the AngularVelocity and the Torque can be connected sepa-rately (PUMPROTATIONALSPEED).

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    VariablePumpRotationalSpeed

    Symbol

    Sketch

    p1

    p2

    InternalLeakage

    Input

    InertiaMomentViscousDamping

    RotationalSpeedTorque

    EthaHMDisplacementVolume

    RotationalSpeedTorque

    +ExternalLeakage

    ExternalLeakage

    Connectors and Variables

    Name Type Unit Description

    p1 Hydr bar pressure 1

    p2 Hydr bar pressure 2

    RotationalSpeed In 1/min input of rotational speed

    Input In - signal for the control of the

    pump displacement

    LoadTorque Out Nm required torque of the drive at

    predefined rotational speed

    VolumeFlow V - auxiliary variable

    Parameters

    Name Value Unit Description

    DisplacementVolume 32 cm displacement volume at a rota-

    tion of the pump without leak-

    age

    InertiaMoment 0.05 kgm inertia moment of working parts

    of the pump

    ViscousDamping 1 Nms speed-dependent damping

    InternalLeakage 0.01 l/min/bar internal leakage

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    Name Value Unit Description

    ExternalLeakage 0 l/min/bar theoretical pump delivery

    EthaHM 1 - hydro-mechanical

    DifferentiationTime 1 ms auxiliary variable

    PrefixMomentum -1 - prefix of output

    InputMin -1 - standardization parameter for

    the input signal

    InputMax 1 - standardization parameter for

    the input signal

    CavitationPressure -0.5 Bar Pressure limit at which cavita-

    tion starts

    Notes

    The component part VARIABLEPUMPROTATIONALSPEED constitutes a model of a displacement pump in which the RotationalSpeed is predefined and the required Torque of the drive is calculated. Inertia and friction momentum are considered.

    The Torque is differentiated from the spin equation. This demands the parameter Differ-entiationTime.

    By means of the parameter PrefixMomentum the prefix of the momentum can be adjusted according to the requirements for the connection to further component parts.

    Depending on the direction of the rotation, both p1 and p2 can designate the high pres-sure side of then pump. (Irrespective of the delivery direction) The VolumeFlow on princi-ple refers to the connection p1.

    A model of a displacement pump with variable angular velocity is also available as a com-ponent part in which the connections for the AngularVelocity and the Torque are united in one mechanical connection (VARIABLEPUMPROTATIONALSPEEDMECH).

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    VariablePumpRotationalSpeedMech

    Symbol

    Sketch

    pP

    pT

    InternalLeakage

    InertiaMomentViscousDamping

    MechTorque

    DisplacementVolumeEthaHM

    MechomegaMechM, Torque

    +Input

    ExternalLeakage

    ExternalLeakage

    Connectors and Variables

    Name Type Unit Description

    p1 Hydr bar working pressure

    p2 Hydr bar reservoir pressure

    Input In - signal for the control of the

    pump displacement

    Mech

    Mechomega

    MechM

    Mech

    In

    Out

    -

    deg/s

    Nm

    mechanical connection

    angular velocity

    required torque

    VolumeFlow Out l/min delivery

    Parameters

    Name Value Unit Description

    DisplacementVolume 32 cm displacement volume at a rota-

    tion of the pump without leak-

    age

    InertiaMoment 0.05 kgm inertia moment of working parts

    of the pump

    ViscousDamping 1 Nms speed-dependent damping

    InternalLeakage 0.01 l/min/bar internal leakage

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    Name Value Unit Description

    ExternalLeakage 0 l/min/bar theoretical pump delivery

    EthaHM 1 - hydro-mechanical efficiency

    DifferentiationTime 1 ms help parameter for calculation of

    the momentum

    InputMin -1 - standardization parameter for

    the input signal

    InputMax 1 - standardization parameter for

    the input signal

    CavitationPressure -0.5 Bar Pressure limit at which cavita-

    tion starts

    PrefixMomentum -1 - prefix of output

    Notes

    The component part VARIABLEPUMPROTATIONALSPEEDMECH constitutes a model of a displace-ment pump in which the RotationalSpeed is predefined and the required Torque of the drive is calculated. Inertia and friction momentum are considered. The connections for the angular velocity (Mechomega) and the output torque (MechM) are united in the mechani-cal connection Mech.

    The Torque is differentiated from the spin equation. This demands the parameter Differ-entiationTime.

    By means of the parameter PrefixMomentum the prefix of the Torque can be adjusted according to the requirements for the connection to further component parts.

    Depending on the direction of the rotation, both pP and pT can designate the high pres-sure side of the pump. (Irrespective of the delivery direction) The VolumeFlow on princi-ple refers to the connection pP.

    A model of a pump with variable angular velocity is also available as a component part in which the connections for the AngularVelocity and the Torque can be connected sepa-rately (PUMPROTATIONALSPEED).

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    PressureControlledPump

    Symbol

    Sketch

    pP

    pT

    InternalLeakage

    1/ControllerResponseTime

    -

    DefaultPressureExternalLeakage

    ExternalLeakage

    Connectors and Variables

    Name Type Unit Description

    pP Hydr bar working pressure

    pT Hydr bar reservoir pressure

    VolumeFlow Out l/min delivery

    PMaxVar In kW external maximum pump power

    default

    Parameters

    Name Value Unit Description

    VolumeFlow 30 l/min delivery at total displacement of

    the pump without leakage

    InternalLeakage 0.001 l/min/bar internal leakage

    ExternalLeakage 0 l/min/bar theoretical pump delivery

    ControllerResponseTime 100 ms time constant for the control

    system

    DefaultPressure 100 bar default pressure of the pump

    Adjustmentmin 0 % Minimum pump adjustment

    Adjustmentmax 100 % Maximum pump adjustment

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    Name Value Unit Description

    CavitationPressure -0.5 Bar Pressure limit at which cavita-

    tion starts

    PMax 100 kW Maximum power

    Notes

    The component part PRESSURECONTROLLEDPUMP constitutes a model that represents a pres-sure controlled pump according to its control parameters. The pressure control comes up

    to a PT1-controler with a time constant ControllerResponseTime. During the simulation the nominal pressure of the pump stays constant.

    (Irrespective of the delivery direction) The VolumeFlow on principle refers to the connec-tion pP.

    A model of a pressure controlled pump is also available as a component part in which the nominal pressure is variable during the simulation (VARIABLEPRESSURECONTROLLEDPUMP).

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    VariablePressureControlledPump

    Symbol

    Sketch

    pP

    pT

    InternalLeakage

    1/ControllerResponseTime

    -

    Input DefaultPressure

    ExternalLeakage

    ExternalLeakage

    Connectors and Variables

    Name Type Unit Description

    PP Hydr bar working pressure

    PT Hydr bar reservoir pressure

    Input In - input signal to adjust the nomi-

    nal pressure

    VolumeFlow Out l/min delivery

    PMaxVar In kW external maximum pump power

    default

    Parameters

    Name Value Unit Description

    VolumeFlow 30 l/min delivery at total displacement of

    the pump without leakage

    DefaultPressure 100 bar default pressure of the pump

    InternalLeakage 0.001 l/min/bar internal leakage

    ExternalLeakage 0 l/min/bar theoretical pump delivery

    ControllerResponseTime 100 ms time constant for the control

    system

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    Name Value Unit Description

    InputMin 0 - standardization parameter for

    the input signal

    InputMax 1 - standardization parameter for

    the input signal

    Adjustmentmin 0 %

    Adjustmentmax 0 %

    CavitationPressure -0.5 bar Pressure limit at which cavita-

    tion starts

    Pmax 100 kW Maximum power

    Notes

    The component part VARIABLEPRESSURECONTROLLEDPUMP constitutes a model that represents a pressure controlled pump according to its control parameters. The pressure control

    comes up to a PT1-controler with a time constant ControllerResponseTime. During the simulation the nominal pressure of the pump stays constant.

    (Irrespective of the delivery direction) The VolumeFlow on principle refers to the connec-tion pP.

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    PumpCharacteristic

    Symbol

    Sketch

    pP

    pT

    VolumeFlow CharacteristicQdepP

    Factor

    Connectors and Variables

    Name Type Unit Description

    pP Hydr bar working pressure

    pT Hydr bar reservoir pressure

    VolumeFlow Out l/min delivery

    Parameters

    Name Value Unit Description

    CharacteristicQdepP - - look-up-table, which describes

    the flow in dependence on the

    pressure difference

    Factor 1 - factor to squeeze or stretch the

    look-up-table

    Notes

    The component part PUMPCHARACTERISTICS constitutes a model that represents a flow source which describes the flow in dependence on the applied pressure differenc pP - pT via a look-up-table.

    VolumeFlow = Factor f CharacteristicQdepP (pP - pT)

    (Irrespective of the delivery direction) The VolumeFlow on principle refers to the connec-tion pP.

    The look-up-table can be compressed and/or stretched via the parameter Factor. In case the pressure difference is more than- or falls below the range of the look-up-table, it is calculated with the respective boundary value the look-up-table.

    A model of an unchangeable pump is also available as a component, with that the flow is computed from a defaulted VolumeFlow and the leakage. (Pump).

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    VariablePumpCharacteristic

    Symbol

    Sketch

    p1

    p2

    Input

    VolumeFlow CharacteristicQdepPdepXFactor

    Connectors and Variables

    Name Type Unit Description

    p1 Hydr bar pressure 1

    p2 Hydr bar pressure 2

    Input In - signal to control the pump dis-

    placement

    VolumeFlow Out l/min delivery

    Parameters

    Name Value Unit Description

    CharacteristicQdepPdepX - - look-up-table, which describes

    the flow in dependence on the

    pressure difference

    Factor 1 - factor to squeeze or stretch the

    look-up-table

    Notes

    The component part PUMPCHARACTERISTICS constitutes a model that represents a flow source which describes the flow in dependence on the applied pressure differenc pP - pT and an input signal (Input) via the two dimensional look-up-table CHAR-ACTERISTICQDEPPDEPX.

    VolumeFlow = Factor f CHARACTERISTICQDEPPDEPX (p1 - p2, Input)

    The pressure difference p1 - p2 is defined as Input 1 and Input as Input 2 of the look-up-table.

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    Depending on the direction of the rotation, both p1 and p2 can designate the high pres-sure side of the pump. (Irrespective of the delivery direction) The VolumeFlow on princi-ple refers to the connection p1.

    The look-up-table can be compressed and/or stretched via the parameter Factor. In case the pressure difference is more than- or falls below the range of the look-up-table, it is calculated with the respective boundary value the look-up-table.

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    PistonPump

    Symbol

    Sketch

    pP

    pT

    InternalLeakage

    ExternalLeakage

    ExternalLeakage

    DisplacementVolumeNoOfPistonsCavitationPressurePhi

    Connectors and Variables

    Name Type Unit Description

    pP Hydr bar working pressure

    pT Hydr bar reservoir pressure

    Flow Out l/min delivery

    Speed Out 1/min specified speed

    Parameters

    Name Value Unit Description

    DisplacementVolume 10 cm Displacement volume

    NoOfPistons 1 1 Number of pistons

    InternalLeakage 0.001 l/min/bar Internel leakage of the pump

    ExternalLeakage 0 l/min/bar Extenal leakage of the pump

    CavitationPressure -0.5 bar Pressure limit at which cavita-

    tion starts

    Phi 0 deg Angle of the pistons

    Notes

    The component PISTONPUMP constitutes a model that represents a flow source which de-scribes the flow in dependence on the applied pressure differenc pP - pT and an input Speed.

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    VariablePistonPump

    Symbol

    Sketch

    pP

    pT

    InternalLeakage

    ExternalLeakage

    ExternalLeakage

    DisplacementVolumeNoOfPistonsInputMaxInputMinCavitationPressurePhi

    Connectors and Variables

    Name Type Unit Description

    p1 Hydr bar pressure 1

    p2 Hydr bar pressure 2

    Input In - signal to control the pump dis-

    placement

    Flow Out l/min delivery

    Speed Out 1/min Specified speed

    Parameters

    Name Value Unit Description

    DisplacementVolume 10 cm Displacement volume

    NoOfPistons 1 1 Number of pistons

    InputMax 1 1 Standard maximum value of the

    Input signal

    InputMin -1 1 Standard minimum value of the

    Input signal

    InternalLeakage 0.001 l/min/bar Internal leakage in the pump

    ExternalLeakage 0 l/min/bar External leakage in the pump

    CavitationPressure -0.5 bar Pressure limit at which cavita-

    tion starts

    Phi 0 deg Angle of the pistons

  • Hydraulics

    24 2008 FLUIDON GmbH

    Notes

    The component VARIABLEPISTONPUMP is a model of an variable pump with different volume flow pulsation, which depends on the number of pistons, revolution and the input signal.

    For the Volumeflow:

    Input = 0 -> Volumeflow = 0

    Input = 1 -> Volumeflow = Qmax

    Input = 0 < n < 1 -> Volumeflow = 0 < Q < Qmax

  • Hydraulics

    2008 FLUIDON GmbH 25

    Motors

    Rotational Motors

    HydroMotor

    Symbol

    Sketch

    p2

    p1

    InternalLeakage

    InertiaMoment

    ViscousDamping

    LoadTorqueRotationalSpeedAngularVelocityAngleMech

    LoadTorque, MechMRotationalSpeed, Mechomega,AngularVelocity, Angle,Mechphi

    +

    DisplacementVolume

    ExternalLeakage

    ExternalLeakage

    Connectors and Variables

    Name Type Unit Description

    p1 Hydr bar pressure 1

    p2 Hydr bar pressure 2

    Mech

    MechM

    Mechphi

    Mechomega

    Mech

    In

    Out

    Out

    -

    Nm

    deg

    deg/s

    mechanical connector

    torque at the motor

    angle

    angular velocity

    LoadTorque In Nm torque at the motor

    RotationalSpeed Out 1/min rotational speed of the motor

    Angle Out deg Angle of the motor

    VolumeFlow Out l/min flow at connector p1

    AngleDot Out rad/s Angular velocity of the motor

  • Hydraulics

    26 2008 FLUIDON GmbH

    Parameters

    Name Value Unit Description

    DisplacementVolume 50 cm displacement volume of the mo-

    tor

    InertiaMoment 1 kgm inertia momentum of working

    parts of the motor

    ViscousDamping 1 Nms velocity depending damping

    InternalLeakage 0.001 l/min/bar internal leakage

    ExternalLeakage 0 l/min/bar external leakage

    Notes

    The component HYDROMOTOR is the model of a hydraulic constant motor.

    Depending on the sense of rotation, both p1 and p2 can designate the high pressure side of the motor. If p1 > p2 a positive sense of rotation results. If LoadTorque > 0 a positive acceleration results.

    Volumeflow refers (independent of the sense of rotation) fundamentally to the connector p1.

    At the mechanical connector Mech of the HYDROMOTOR the angle of the motor (Mechphi), the rotational speed (Mechomega) and the load torque (MechM) are summarized.

  • Hydraulics

    2008 FLUIDON GmbH 27

    HydroTwinMotor

    Symbol

    Sketch

    p1

    InertiaMoment 1 +InertiaMoment 2ViscousDamping 1 +ViscousDamping 2

    LoadTorqueRotationalSpeedAngleMech

    LoadTorque, MechMRotationalSpeed, MechomegaAngle, Mechphi

    +

    DisplacementVolume 2

    p3

    p4

    Internal-Leakage1

    Internal-Leakage2

    External-Leakage1

    External-Leakage2

    External-Leakage1

    External-Leakage2p2

    DisplacementVolume1

    1 2

    Connectors and Variables

    Name Type Unit Description

    p1 Hydr bar pressure 1

    p2 Hydr bar pressure 2

    p3 Hydr bar pressure 3

    p4 Hydr bar pressure 4

    Mech

    MechM

    Mechphi

    Mechomega

    Mech

    In

    Out

    Out

    -

    Nm

    deg

    deg/s

    mechanical connector

    torque at the motor

    angle

    angular velocity

    LoadTorque In Nm torque at the motor

    RotationalSpeed Out 1/min rotational speed of the motor

    Angle Out deg angle of the motors

    Volumenflow1 Out l/min flow at connector p1

    Volumenflow2 Out l/min flow at connector p3

    AngleDot Out rad/s Angular velocity of the motor

  • Hydraulics

    28 2008 FLUIDON GmbH

    Name Type Unit Description

    MotorTorque1 Out Nm torque of the motor 1

    MotorTorque2 Out Nm torque of the motor 2

    Parameters

    Name Value Unit Description

    DisplacementVolume1 50 cm displacement volume of the mo-

    tor (motor 1)

    DisplacementVolume2 50 cm displacement volume of the mo-

    tor (motor 2)

    InertiaMoment1 1 kgm inertia momentum of working

    parts of the motor 1

    InertiaMoment2 1 kgm inertia momentum of working

    parts of the motor 2

    ViscousDumping1 1 Nms velocity depending damping

    (motor 1)

    ViscousDumping2 1 Nms velocity depending damping

    (motor 2)

    InternalLeakage1 0.001 l/min/bar internal leakage (motor 1)

    InternalLeakage2 0.001 l/min/bar internal leakage (motor 2)

    ExternalLeakage1 0 l/min/bar external leakage (motor 1)

    ExternalLeakage2 0 l/min/bar external leakage (motor 2)

    Notes

    The component HYDROTWINMOTOR is the model of two hydraulic constant motors that are assembled on one shaft. In addition, a hydraulic transformer can be realized with the component.

    Depending on the sense of rotation, both p1 and p3 and p2 and p4 can designate the high pressure side of the motor. If p1 > p2 or p3 > p4 a positive sense of rotation results. If LoadTorque > 0 a positive acceleration results.

    Volumeflow1 refers (independent of the sense of rotation) fundamentally to the connector p1, the Volumeflow2 on p3.

    At the connectors MotorTorque1 and MotorTorque2, the torque transferred effectively by the motors can be obtained.

    At the mechanical connector Mech of the HYDROTWINMOTOR the angle of the motor (Mech-phi), the rotational speed (Mechomega) and the load torque (MechM) are summarized.

  • Hydraulics

    2008 FLUIDON GmbH 29

    HydroVariableMotor

    Symbol

    Sketch

    p2

    p1

    InternalLeakage

    InertiaMoment

    ViscousDamping

    LoadTorqueRotationalSpeedAngularVelocityAngleMech

    LoadTorque, MechMRotationalMoment, MechomegaAngularVelocity,Angle, Mechphi

    +

    DisplacementVolume

    InputExternalLeakage

    ExternalLeakage

    Connectors and Variables

    Name Type Unit Description

    p1 Hydr bar pressure 1

    p2 Hydr bar pressure 2

    Mech

    MechM

    Mechphi

    Mechomega

    Mech

    In

    Out

    Out

    -

    Nm

    deg

    deg/s

    mechanical connector

    torque at the motor

    angle

    angular velocity

    LoadTorque In Nm torque at the motor

    Input In - input signal for the displacement

    of the motor

    RotationalSpeed Out 1/min rotational speed of the motor

    VolumeFlow Out l/min flow at connector p1

    Angle Out deg angle of the motors

    AngleDot Out Rad/S Angular velocity of the motor

  • Hydraulics

    30 2008 FLUIDON GmbH

    Parameters

    Name Value Unit Description

    DisplacementVolume 50 cm displacement volume of the mo-

    tor

    InertiaMoment 1 kgm inertia momentum of working

    parts of the motor

    ViscousDamping 1 Nms velocity depending damping

    InternalLeakage 0.001 l/min/bar internal leakage

    ExternalLeakage 0 l/min/bar external leakage

    InputMin -1 - standardization parameter for

    the input signal

    InputMax 1 - standardization parameter for

    the input signal

    Notes

    The component HYDROVARIABLEMOTOR is the model of a hydraulic motor with a variable displacement.

    Depending on the sense of rotation, both p1 and p2 can designate the high pressure side of the motor. If p1 > p2 a positive sense of rotation results. If LoadTorque > 0 a positive acceleration results.

    Volumeflow refers (independent of the sense of rotation) fundamentally to the connector p1.

    At the mechanical connector Mech of the HYDROMOTOR the angle of the motor (Mechphi), the rotational speed (Mechomega) and the load torque (MechM) are summarized.

  • Hydraulics

    2008 FLUIDON GmbH 31

    HydroMotorWithFriction

    Symbol

    Sketch

    p2

    p1

    InternalLeakage

    InertiaMoment

    LoadTorqueRotationalSpeedAngularSpeedAngleMech

    LoadTorque, MechMRotationalSpeed, Mechomega,AngularVelocity,Angle, Mechphi

    +

    DisplacementVolume

    BreakawayFrictionTorqueMixedFrictionTorqueRotationalSpeedMixedFrictionViscousDampingRotationalSpeed

    ExternalLeakage

    ExternalLeakage

    Connectors and Variables

    Name Type Unit Description

    p1 Hydr Bar pressure 1

    p2 Hydr bar pressure 2

    Mech

    MechM

    Mechphi

    Mechomega

    Mech

    In

    Out

    Out

    -

    Nm

    deg

    deg/s

    mechanical connector

    torque at the motor

    angle

    angular velocity

    LoadTorque In Nm torque at the motor

    RotationalSpeed Out 1/min rotational speed of the motor

    Angle Out deg Angle of the motor

    AngularVelocity Out deg/min angular velocity of the motor

    VolumeFlow Out l/min flow at connector p1

  • Hydraulics

    32 2008 FLUIDON GmbH

    Parameters

    Name Value Unit Description

    DisplacementVolume 50 cm displacement volume of the mo-

    tor

    BreakawayFrictionTorque 10 Nm characteristic for Stribeck curve

    MixedFrictionTorque 1 Nm characteristic for Stribeck curve

    RotSpeedMixedFriction 1 1/min characteristic for Stribeck curve

    ViscousDampingRotSpeed 1 Nms characteristic for Stribeck curve

    Inertia 0.05 kgm inertia momentum of working

    parts of the motor

    InternalLeakage 0.001 l/min/bar internal leakage

    ExternalLeakage 0 l/min/bar external leakage

    Notes

    The component HYDROMOTORWITHFRICTION is the model of a hydraulic constant motor. Within this model the velocity depending friction is modeled, too.

    The friction is modeled in accordance to the Stribeck curve. The parameters Breakaway-FrictionTorque, MixedFrictionTorque, RotationalSpeedMixedFriction and ViscousDampin-gRotationalSpeed represents the characteristic values shown in the figure. The friction is independent on the pressure.

    BreakawayFrictionTorque

    MixedFrictionTorque

    RotationalSpeedMixedFriction

    ViscousDampingRotationalSpeed

    RotationalSpeed

    FrictionTorque

    Depending on the sense of rotation, both p1 and p2 can designate the high pressure side of the motor. If p1 > p2 a positive sense of rotation results. If LoadTorque > 0 a positive acceleration results.

    Volumeflow refers (independent of the sense of rotation) fundamentally to the connector p1.

    At the mechanical connector Mech of the HYDROMOTORWITHFRICTION the angle of the motor (Mechphi), the rotational speed (Mechomega) and the load torque (MechM) are summa-rized.

  • Hydraulics

    2008 FLUIDON GmbH 33

    SwivelDrive

    Symbol

    Sketch

    Axial-Diameter

    Fla

    nkD

    iam

    ete

    rMaxim

    um-

    Swivelrange

    MassinertiaTorque

    Frictionfactor_Axialstrip

    ExterneLeckage

    BrakeawaytoPerLength_LeverMixedfrictiontoPerLength_LeverMeafrictiontoPerLength_LeverMixedfrictionomegaMeasuringfrictionomega

    AngleMin

    0

    Angle

    max

    Angle

    Frictionfactor_Flankseal

    InternalLeakage

    p1

    p2

    Angle, MechphiAngleVelocity, MechomegaAngleAccelerationLoadTorque, MechM

    ++++

    Connectors and Variables

    Name Type Unit Description

    p1 Hydr Bar pressure 1

    p2 Hydr bar pressure 2

    Mech

    MechM

    Mechphi

    Mechomega

    Mech

    In

    Out

    Out

    -

    Nm

    deg

    deg/s

    mechanical connector

    torque at the motor

    angle

    angular velocity

    VolumeFlow1 Out l/min flow at connector p1

  • Hydraulics

    34 2008 FLUIDON GmbH

    Name Type Unit Description

    VolumefFlow2 Out l/min flow at connector p2

    AngularAcceleration Out deg/min angular acceleration of the mo-

    tor

    AngularVelocity Out deg/min angular velocity of the motor

    Angle Out deg Angular displacement of the mo-

    tor

    LoadTorque In Nm torque at the motor

    Parameters

    Name Value Unit Description

    AxialDiameter 24 mm Diameter of the swivel axis

    FlankDiameter 50 mm Diameter of the pump

    FlankLength 20 mm Length of the Vane

    MaximumSwivelrange 180 deg Swivel range of the Pump

    AngleMin 0 deg Minimum angle

    AngleMax 180 deg Maximum Angle

    MassinertiaTorque 1.0E-4 Kgm Mass Inertia torque of the Pump

    BrakeawaytoPer-

    Length_Lever

    0 Nm/mm Characteristic value of Stribeck

    curve

    MixedfrictiontoPer-

    Length_Lever

    0 Nm/mm Characteristic value of Stribeck

    curve

    MeafrictiontoPer-

    Length_Lever

    0 Nm/mm Characteristic value of Stribeck

    curve

    Mixedfrictionomega 0.000

    1

    deg/s Characteristic value of Stribeck

    curve

    Measuringfrictionomega 0.000

    2

    deg/s Characteristic value of Stribeck

    curve

    Frictionfactor_Flankseal 0.5 1/bar Pressure dependent friction fac-

    tor of the Flankseal

    AvailableAxialsealing 0

    Frictionfactor_Axialstrip 0.5 1/bar Pressure dependent friction fac-

    tor of the axial strip

    ExternalLeakage1 0 l/min/bar External pressure dependent

    Leakage

    ExternalLeakage2 0 l/min/bar External pressure dependent

    Leakage

    InternalLeakage 0 l/min/bar Internal pressure dependent

    Leakage

  • Hydraulics

    2008 FLUIDON GmbH 35

    Notes

    The component SWIVELDRIVE is a modell of an Hydraulic swivel motor in which the fric-tional torque of the vane anf Axial Seal has been calculated using the stribeck friction curve.

    The component has been constructed based on the Swivel drive where by the characteris-tic values have been parameterized.

    The parameter maximum swivelling range specifies the greatest possible angle of rotation of the vane drive. Over Anglemin and Anglemax notices can be stopped in this range, whereby angle min and angle max must be positive. Angle min is > 0 and angle max < maximum swivelling range remains to dead volumes in the chambers, if the wing drives into one of the notices.

    In the Stribeck curves, over which the friction moments of the wing and Axial seals to be determined are calculated over the length of the seals and on the associated lever arms by the application of Angularvelocity. The seal between Vane and housing, which seals, and separates the two chambers of the vane drive at the axle, and the sealing which seals between axle and housings, which avoid a fluid leakage from the engine,should be taken care of. If the parameter Available Axial sealing is set to zero, the friction moment of the axial sealings is neglected.

    The Stribeck curves are produced for mixing friction omega and measuring friction omega for a difference of pressure by 0 bar from the characteristic values

    The pressure dependence of the friction moments is calculated over the parameter factors (FricitonFactor_FlankSeal and/or FrictionFactor_AxialSeal):

    FrictionmomentPressuredifference 0 =

    = FrictionmomentPressuredifference = 0 (1 + |Pressuredifference| Factor)

    In the following picture the Stribeck curve is represented:

    BrakeawayMoProLength_Lever

    MixedfrictiontoPerLength_Lever

    Mixedfrictionomega Angularvelocity

    Frictionmoment per SealLength

    Measuringfrictionomega

    MeafrictiontoPerLength_Lever

    Pressuredifference = 0 bar

    PressuredifferenceFrictionFactor_AxialSealFricitonFactor_FlankSeal

    In the mechanical connection Mech of the component, the angle, the angular velocity, and the Load torque has been represnted.

  • Hydraulics

    36 2008 FLUIDON GmbH

    Linear Motors

    Cylinder

    Symbol

    Sketch

    InternalLeakage

    ExternalLeakage1ExternalLeakage2

    BreakawayFrictionForceMixedFrictionforce

    SpeddMixedFrictionViscousDamping

    FrictionCharacteristic

    p1 p2

    Load

    RodDiameter1

    PistonDiameter

    RodDiameter2

    SpringStiffness1SpringLength1

    SpringStiffness2SpringLength2

    Orientation

    Stroke, Mechx,Velocity, Mechv,Acceleration,Load, MechF

    strokemin strokemax0

    VelocityStrokeMechAcceleration

    Mass

    Connectors and Variables

    Name Type Unit Description

    p1 Hydr bar pressure 1

    p2 Hydr bar pressure 2

    Load In N force at the piston

    Mech

    MechF

    Mechx

    Mechv

    Mech

    In

    Out

    Out

    -

    N

    mm

    m/s

    mechanical connection

    force at the piston

    stroke of the piston

    velocity of the piston

    MechPipe

    MechF

    Mechx

    Mechv

    Mech

    Out

    In

    In

    -

    N

    Mm

    m/s

    mechanical connection

    inner force at the cylinder-

    pipe

    Stroke of the cylinder pipe

    Velocity of the cylinder pipe

    Acceleration Out m/s2 acceleration of the piston

  • Hydraulics

    2008 FLUIDON GmbH 37

    Name Type Unit Description

    Velocity V m/s velocity of the piston

    Stroke Out mm stroke of the piston

    Parameters

    Name Value Unit Description

    PistonDiameter 100 mm diameter of the piston

    RodDiameter1 50 mm diameter of rod 1

    RodDiameter2 0 mm diameter of rod 2

    Mass 10 kg mass of pistons and piston rods

    Orientation 0 deg angle between the movement

    plane and the horizontal plane

    InternalLeakage 0.001 l/min/bar internal leakage

    ExternalLeakage1 0 l/min/bar theoretical piston delivery at

    piston rod 1

    ExternalLeakage2 0 l/min/bar theoretical piston delivery at

    piston rod 2

    BreakawayFrictionForce 100 N characteristic for Stribeck curve

    MixedFrictionForce 10 N characteristic for Stribeck curve

    SpeedMixedFriction 0.1 m/s characteristic for Stribeck curve

    ViscousDamping 10 Ns/m characteristic for Stribeck curve

    FrictionCharacteristic - - one dimensional look-up table

    for the velocity dependant fric-

    tion description

    strokemax 100 mm maximum stroke of the piston in

    positive direction

    strokemin -100 mm maximum stroke of the piston in

    negative direction

    SpringStiffness1 0 N/mm stiffness of spring 1

    SpringLength1 0 mm active length of spring 1

    SpringStiffness2 0 N/mm stiffness of spring 2

    SpringLength2 0 mm active length of spring 2

    FluidMassConsideration 0 - consideration of fluid mass in

    the dynamic system calculation

    (1=on ; 0=off)

    Notes

    The component CYLINDER is the model of a synchronizing or differential cylinder which has two hydraulic ports. If a differential cylinder is required, one rod diameter (RodDiameter1 or RodDiameter2) must only be parameterized with zero. In this case, the external leak-age (ExternalLeakage1 or ExternalLeakage2) is automatically set to zero for this cylinder side. The symbol for the cylinder can be a synchronizing or a differential cylinder.

  • Hydraulics

    38 2008 FLUIDON GmbH

    The friction force is computed in accordance to the Stribeck curve. The parameters BreakawayFrictionForce, MixedFrictionForce, SpeedMixedFriction, and the ViscousDamping represents the characteristic values shown in the figure. The friction is not influenced by the inclination of the movement plane and it is independent on the pressure.

    Acceleration

    FrictionBreakawayFrictionForce

    MixedFrictionForce

    SpeedMixedFriction

    ViscousDamping

    The friction force is also definable with a look-up table FFriction(v). The friction is also defin-able with a look-up table (Ffriction(v). If a table is selected it will be used, if not, the normal parameters for the friction description are used. The look-up table is defined in one quar-ter only for positive velocity include 0. The component calculates with the absolute value. The mechanical connector Mech transmits the variables MechF as well as stroke Mechx and velocity Mechv summarized.

    Accompiend by the mechanical connector MechPipe the cylinder is supported against the environment. Because of the massless cylinderpipe in the modell , an external mass has to be connected. This external mass again has to be supported with a spring surrendered against the environment.

    With the Orientation, the movement plane can be sloped in any angle to the horizontal. The resulting force due to gravity is considered automatically.

    The parameter SpringLength represents the active length of a spring, that is the overall length minus the inactive length. The following figure shows the diagram of a cylinder in which the inactive lengths of the springs are also drawn in:

    inactiveSpringLength

    activeSpringLength

    activeSpringLength

    inactiveSpringLength

    stroke of the piston

    strokemin strokemax

    stroke

    The overall length of the spring is measured in the non-artesian state. It is possible that the active spring length (SpringLength1 or SpringLength2) is larger than the stroke of the piston (strokemax - strokemin). In this case the springs have a permanent pre-tension. Otherwise, the springs are not continually in contact with the piston.

    With the help of the parameter FluidMassConsideration the influence of the fluid mass on the system behaviour could be taken into consideration. The weight force as well as the mass inertia of the relevant part of fluid, depending on cylinder orientation and piston position, are intergrated into the system calculation.

  • Hydraulics

    2008 FLUIDON GmbH 39

    Cylinder4Areas

    Symbol

    Sketch

    InternalLeakage1to2

    ExternalLeakage1 ExternalLeakage4

    BreakawayFrictionForceSpeedMixedFriction

    MixedFrictionViscousDamping

    p1 p3

    Load

    RodDiameter1

    PistonDiameter

    RodDiameter4SpringStiffness1

    SpringLength1SpringStiffness4SpringLength4

    p4p2

    InternalLeakage2to3InternalLeakage3to4RodDiameter3RodDiameter2

    Stroke,VelocityAcceleration

    strokemin strokemax0

    Orientation

    StrokeVelocityAcceleration

    Mass

    Connectors and Variables

    Name Type Unit Description

    p1 Hydr bar pressure 1

    p2 Hydr bar pressure 2

    p3 Hydr bar pressure 3

    p4 Hydr bar pressure 4

    Mech

    MechF

    Mechx

    Mechv

    Mech

    In

    Out

    Out

    -

    N

    Mm

    m/s

    mechanical connection

    force at the piston

    stroke of the piston

    velocity of the piston

    Load In N force at the piston

    Acceleration Out m/s2 acceleration of the piston

    Velocity Out m/s velocity of the piston

    Stroke Out mm stroke of the piston

  • Hydraulics

    40 2008 FLUIDON GmbH

    Parameters

    Name Value Unit Description

    PistonDiameter 100 mm diameter of the piston

    RodDiameter1 50 mm diameter of rod 1

    RodDiameter2 70 mm diameter of rod 2

    RodDiameter3 70 mm diameter of rod 3

    RodDiameter4 50 mm diameter of rod 4

    strokemax 100 mm maximum stroke of the piston in

    positive direction

    strokemin -100 mm maximum stroke of the piston in

    negative direction

    Mass 10 kg mass of pistons and piston rods

    Orientation 0 deg angle between the movement

    plane and the horizontal plane

    BreakawayFrictionForce 100 N characteristic for Stribeck curve

    MixedFrictionForce 10 N characteristic for Stribeck curve

    SpeedMixedFriction 0.1 m/s characteristic for Stribeck curve

    ViscousDamping 10 Ns/m characteristic for Stribeck curve

    ExternalLeakage1 0 l/min/bar external leakage at rod 1

    ExternalLeakage4 0 l/min/bar external leakage at rod 1

    InternalLeakage1to2 0.001 l/min/bar internal leakage between cham-

    ber 1 and chamber 2

    InternalLeakage2to3 0.001 l/min/bar internal leakage between cham-

    ber 2 and chamber 3

    InternalLeakage3to4 0.001 l/min/bar internal leakage between cham-

    ber 3 and chamber 4

    SpringLength1 0 mm active length of spring 1

    SpringStiffness1 0 N/mm stiffness of spring 1

    SpringLength4 0 mm active length of spring 4

    SpringStiffness4 0 N/mm stiffness of spring 4

    Notes

    The component CYLINDER4AREAS is the model of a synchronizing or differential cylinder which has four hydraulic ports.

    The friction force is computed in accordance to the Stribeck curve. The parameters BreakawayFrictionForce, MixedFrictionForce, SpeedMixedFriction, and the ViscousDamping represents the characteristic values shown in the figure. The friction is not influenced by the inclination of the movement plane and it is independent on the pressure.

  • Hydraulics

    2008 FLUIDON GmbH 41

    Acceleration

    FrictionBreakawayFrictionForce

    MixedFrictionForce

    SpeedMixedFriction

    ViscousDamping

    With the Orientation, the movement plane can be sloped in any angle to the horizontal. The resulting force due to gravity is considered automatically.

    The parameter SpringLength represents the active length of a spring, that is the overall length minus the inactive length. The following figure shows the diagram of a cylinder in which the inactive lengths of the springs are also drawn in:

    inactiveSpringLength

    activeSpringLength

    activeSpringLength

    inactiveSpringLength

    stroke of the piston

    strokemin strokemax

    stroke

    The overall length of the spring is measured in the non-artesian state. It is possible that the active spring length (SpringLength1 or SpringLength2) is larger than the stroke of the piston (strokemax - strokemin). In this case the springs have a permanent pre-tension. Otherwise, the springs are not continually in contact with the piston.

  • Hydraulics

    42 2008 FLUIDON GmbH

    CylinderVInlet

    Symbol

    Sketch

    InternalLeakage

    ExternalLeakage1 ExternalLeakage2

    p1 p2

    VelocityRodDiameter1

    PistonDiameter

    RodDiameter2SpringStiffness1

    SpringLength1 SpringStiffness2SpringLength2

    StrokeVelocityForce

    strokemin strokemax0

    Orientation

    StrokeForce

    Connectors and Variables

    Name Type Unit Description

    p1 Hydr bar pressure 1

    p2 Hydr bar pressure 2

    Velocity In m/s velocity of the piston

    Stroke Out mm stroke of the piston

    Force Out N Force that the cylinder gener-

    ates

    Parameters

    Name Value Unit Description

    PistonDiameter 100 mm diameter of the piston

    RodDiameter1 50 mm diameter of rod 1

    RodDiameter2 0 mm diameter of rod 2

    InternalLeakage 0.001 l/min/bar internal leakage

    ExternalLeakage1 0 l/min/bar external leakage at rod 1

    ExternalLeakage2 0 l/min/bar external leakage at rod 2

  • Hydraulics

    2008 FLUIDON GmbH 43

    Name Value Unit Description

    strokemax 100 mm maximum stroke of the piston in

    positive direction

    strokemin -100 mm maximum stroke of the piston in

    negative direction

    SpringStiffness1 0 N/mm stiffness of spring 1

    SpringLength1 0 mm active length of spring 1

    SpringStiffness2 0 N/mm stiffness of spring 2

    SpringLength2 0 mm active length of spring 2

    Notes

    The component CYLINDERVINLET is the model of a synchronizing or differential cylinder which has two hydraulic ports. The velocity of the piston is an input value, the force, that the cylinder generates, is an output value.

    If a differential cylinder is required, one rod diameter (RodDiameter1 or RodDiameter2) must only be parameterized with zero. In this case, the external leakage (ExternalLeak-age1 or ExternalLeakage2) is automatically set to zero for this cylinder side. The symbol for the cylinder can be a synchronizing or a differential cylinder.

    The friction force has to be modeled in the connected system (internal or external).

    With the Orientation, the movement plane can be sloped in any angle to the horizontal. The resulting force due to gravity is considered automatically.

    The parameter SpringLength represents the active length of a spring, that is the overall length minus the inactive length. The following figure shows the diagram of a cylinder in which the inactive lengths of the springs are also drawn in:

    inactiveSpringLength

    activeSpringLength

    activeSpringLength

    inactiveSpringLength

    stroke of the piston

    strokemin strokemax

    stroke

    The overall length of the spring is measured in the non-artesian state. It is possible that the active spring length (SpringLength1 or SpringLength2) is larger than the stroke of the piston (strokemax - strokemin). In this case the springs have a permanent pre-tension. Otherwise, the springs are not continually in contact with the piston.

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    44 2008 FLUIDON GmbH

    CylinderXVInlet

    Symbol

    Sketch

    InternalLeakage

    ExternalLeakage1ExternalLeakage2

    p1 p2

    VelocityStroke

    PistonDiameter

    RodDiameter2SpringStiffness1

    SpringLength1 SpringStiffness2SpringLength2

    stroke,StrokeVelocityForce

    strokemin strokemax0

    Force

    RodDiameter1

    Connectors and Variables

    Name Type Unit Description

    p1 Hydr bar Pressure 1

    p2 Hydr bar Pressure 2

    Velocity In m/s velocity of the piston

    Stroke In mm stroke of the piston

    Force Out N Force that the cylinder gener-

    ates

    Parameters

    Name Value Unit Description

    PistonDiameter 100 mm diameter of the piston

    RodDiameter1 0 mm diameter of rod 1

    RodDiameter2 50 mm diameter of rod 2

    InternalLeakage 100 N internal leakage

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    2008 FLUIDON GmbH 45

    Name Value Unit Description

    ExternalLeakage1 0.001 l/min/bar external leakage at rod 1

    ExternalLeakage2 0 l/min/bar external leakage at rod 2

    strokemax 100 mm maximum stroke of the piston in

    positive direction

    strokemin -100 mm maximum stroke of the piston in

    negative direction

    SpringStiffness1 0 N/mm stiffness of spring 1

    SpringLength1 0 mm active length of spring 1

    SpringStiffness2 0 N/mm stiffness of spring 2

    SpringLength2 0 mm active length of spring 2

    Notes

    The component CYLINDERXVINLET is the model of a synchronizing or differential cylinder which has two hydraulic ports. The velocity and the stroke of the piston are an input value, the force, that the cylinder generates, is an output value.

    If a differential cylinder is required, one rod diameter (RodDiameter1 or RodDiameter2) must only be parameterized with zero. In this case, the external leakage (ExternalLeak-age1 or ExternalLeakage2) is automatically set to zero for this cylinder side. The symbol for the cylinder can be a synchronizing or a differential cylinder.

    The friction force has to be modeled in the connected system (internal or external).

    With the Orientation, the movement plane can be sloped in any angle to the horizontal. The resulting force due to gravity is considered automatically.

    The parameter SpringLength represents the active length of a spring, that is the overall length minus the inactive length. The following figure shows the diagram of a cylinder in which the inactive lengths of the springs are also drawn in:

    inactiveSpringLength

    activeSpringLength

    activeSpringLength

    inactiveSpringLength

    stroke of the piston

    strokemin strokemax

    stroke

    The overall length of the spring is measured in the non-artesian state. It is possible that the active spring length (SpringLength1 or SpringLength2) is larger than the stroke of the piston (strokemax - strokemin). In this case the springs have a permanent pre-tension. Otherwise, the springs are not continually in contact with the piston.

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    46 2008 FLUIDON GmbH

    CylinderAreaCharacteristic

    Symbol

    Sketch

    InterneLekage

    ExterneLekage1 ExterneLekage2

    BreakawayfrictioforceSpeedMixedFriction

    MischReibungViscousDamping

    p1 p2

    Last

    CharacteristicPistonArea

    CharacteristicSpring1 CharacteristicSpring2

    stroke, StrokeVelocityAcceleration

    strokemin strokemax0

    Orientation

    MechPipeVelocityStrokeMechAcceleration

    Connectors and Variables

    Name Type Unit Description

    p1 Hydr bar Pressure 1

    p2 Hydr bar Pressure 2

    Load In N force at the piston

    Mech

    MechF

    Mechx

    Mechv

    Mech

    In

    Out

    Out

    -

    N

    mm

    m/s

    mechanical connection

    force at the piston

    stroke of the piston

    velocity of the piston

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    2008 FLUIDON GmbH 47

    Name Type Unit Description

    MechPipe

    MechF

    Mechx

    Mechv

    Mech

    Out

    In

    In

    -

    N

    mm

    m/s

    mechanical connection

    inner force at the cylinder-

    pipe

    Stroke of the cylinderpipe

    Velocity of the cylinderpipe

    Acceleration Out m/s2 Acceleration of the piston

    velocity V m/s velocity of the piston

    stroke V mm stroke of the piston

    Stroke Out mm stroke of the piston

    Chambervolume1 Out - Actual volume of cylinderroom1

    Chambervolume2 Out - Actual volume of cylinderroom2

    Parameters

    Name Value Unit Description

    VolumeResolution 1 Mm diameter of the piston

    strokemax 100 Mm maximum stroke of the piston in

    positive direction

    strokemin -100 mm maximum stroke of the piston in

    negative direction

    Mass 10 kg mass of pistons and piston rods

    Orientation 0 deg angle between the movement

    plane and the horizontal plane

    InternalLeakage 0.001 l/min/bar internal leakage

    ExternalLeakage1 0 l/min/bar theoretical piston delivery at

    piston rod 1

    ExternalLeakage2 0 l/min/bar theoretical piston delivery at

    piston rod 2

    BreakawayFrictionForce 100 N characteristic for Stribeck curve

    SpeedMixedFriction 0.1 m/s characteristic for Stribeck curve

    MixedFrictionForce 10 N characteristic for Stribeck curve

    ViscousDamping 10 Ns/m characteristic for Stribeck curve

    CharacteristicPistonArea -1. characteristic of the stroke de-

    pendent piston area

    CharacteristicSpring1 stroke dependent spring force in

    room 1

    CharacteristicSpring2 -1. stroke dependent spring force in

    room 2

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    Notes

    The component CYLINDERAREACHARACTERISTIC is the model of a synchronizing cylinder which has two hydraulic ports. The variable piston area realizes arbitrary cylinder geometries, like f.e. gum/resin coatings/coverings/films.

    The area of the piston is defined in dependence to stroke through the characteristic Char-acteristicPistonArea and the characteristic has to be between the value strokemin and strokemax.

    To increase the calculation velocity the stroke dependent volume of both cylinder rooms is calculated by simulation and selected/chosen at the running time. The parameter VolumeResolution defines with which stroke dependent resolution the volume values are calculated.

    The friction force is computed in accordance to the Stribeck curve. The parameters BreakawayFrictionForce, MixedFrictionForce, SpeedMixedFriction, and the ViscousDamping represents the characteristic values shown in the figure. The friction is not influenced by the inclination of the movement plane and it is independent on the pressure.

    Velocity

    FrictionBreakawayFrictionForce

    MixedFrictionForce

    SpeedMixedFriction

    ViscousDamping

    With the Orientation, the movement plane can be sloped in any angle to the horizontal. The resulting force due to gravity is considered automatically.

    Springs are possibly deserted to each cylinder room in kind of a stroke dependent spring force characteristic(parameters CharacteristicSpring 1 and CharacteristicSpring 2). So even non linear spring force progressions like f.e. gum/resin coatings/coverings/films can be mapped comfortable/easy.

    In the mechanical connector Mech of the component the stroke of the cylinders (Mechx), the velocity (Mechv) and the load (MechF) are sumarized.

    Accompiend by the mechanical connector MechPipe the cylinder is supported against the environment. Because of the massless cylinderpipe in the modell , an external mass has to be connected. This external mass again has to be supported with a spring surrendered against the environment.

    If the cylinder is in an inclinate position the Orientation serves to consider the massforce.

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    Directional Valves

    2-x Valves

    SwitchingValve22

    Symbol

    Sketch

    pP

    pAVolumeFlowPressureDifference

    Input

    Overlap

    Stroke

    Strokemin0Strokemax

    Connectors and Variables

    Name Type Unit Description

    pP Hydr bar supply pressure

    pA Hydr bar working pressure

    Input In - input signal for the spool stroke

    Stroke Out mm spool stroke

    VolumeFlow Out l/min flow through the valve

    Parameters

    Name Value Unit Description

    VolumeFlow 30 l/min flow through one metering edge

    at PressureDifference

    PressureDifference 35 bar see above

    Strokemax 1 mm maximum spool stroke for a

    positive stroke

    Strokemin 0 mm maximum spool stroke for a

    negative stroke

    SwitchingTimeOpen 3 ms time for opening motion

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    Name Value Unit Description

    SwitchingTimeClose 3 ms time for closing motion

    SwitchingThreshold 0 - Value of the input signal to open

    the valve

    Overlap 0 % relative overlap of the metering

    edge

    Notes

    The component SWITCHINGVALVE22 is a model of a 2-way switching valve at which the flow characteristic is parameterized over the parameters VolumeFlow, PressureDifference and Overlap.

    The following rule is effective:

    Overlap < 0: valve opened in resting position Overlap = 0: valve just closed in resting position Overlap > 0: valve closed in resting position

    For Input > 0 the valve switches in positive direction up to Stroke = Strokemax, for Input 0 the valve switches in negative direction up to Stroke = Strokemin. The opening of the valve lasts always SwitchingTimeOpen, the closing always SwitchingTimeClose.

    The component SWITCHINGVALVE22 does not represent a physical model of the valve but only its characteristic properties. Therefore the physical properties (e. g. mass of the spool, stiffness of the spring) are not parameterized.

    In addition, a model of this 2-way switching valve is also available as a component, at which the flow characteristic is parameterized with a look-up table (SWITCHING-VALVE22CHARACTERISTICS).

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    SwitchingValve22NO

    Symbol

    Sketch

    pP

    pAVolumeFlowPressureDifference

    Input

    Overlap

    Stroke

    Strokemin0Strokemax

    Connectors and Variables

    Name Type Unit Description

    pP Hydr bar supply pressure

    pA Hydr bar working pressure

    Input In - input signal for the spool stroke

    Stroke Out mm spool stroke

    VolumeFlow Out l/min flow through the valve

    Parameters

    Name Value Unit Description

    VolumeFlow 30 l/min flow through one metering edge

    at PressureDifference

    PressureDifference 35 bar see above

    Strokemax 1 mm maximum spool stroke for a

    positive stroke

    Strokemin 0 mm maximum spool stroke for a

    negative stroke

    SwitchingTimeOpen 3 ms time for opening motion

    SwitchingTimeClose 3 ms time for closing motion

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    52 2008 FLUIDON GmbH

    Name Value Unit Description

    SwitchingThreshold 0 - Value of the input signal to open

    the valve

    Overlap 0 % relative overlap of the metering

    edge

    Notes

    The component SWITCHINGVALVE22NO is a model of a 2-way switching valve at which the flow characteristic is parameterized over the parameters VolumeFlow, PressureDifference and Overlap. The valve is normally open.

    The following rule is effective:

    Overlap < 0: valve opened in resting position Overlap = 0: valve just closed in resting position Overlap > 0: valve closed in resting position

    For Input > 0 the valve switches in positive direction up to Stroke = Strokemax, for Input 0 the valve switches in negative direction up to Stroke = Strokemin. The opening of the valve lasts always SwitchingTimeOpen, the closing always SwitchingTimeClose.

    The component SWITCHINGVALVE22NO does not represent a physical model of the valve but only its characteristic properties. Therefore the physical properties (e. g. mass of the spool, stiffness of the spring) are not parameterized.

    In addition, a model of this 2-way switching valve is also available as a component, at which the valve is normally closed (SWITCHINGVALVE22) and at which the flow characteristic is parameterized with a look-up table (SWITCHINGVALVE22CHARACTERISTICS).

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    SwitchingValve22Characteristics

    Symbol

    Sketch

    pP

    pA

    Input

    CharacteristicEdgePAOverlapStrokePA

    AlphaDPA

    Stroke

    Strokemin0Strokemax

    Connectors and Variables

    Name Type Unit Description

    pP Hydr bar supply pressure

    pA Hydr bar working pressure

    Input In - input signal for the spool stroke

    Stroke Out mm spool stroke

    VolumeFlow Out l/min volume flow

    Parameters

    Name Value Unit Description

    Strokemax 1 mm maximum spool stroke for a

    positive stroke

    Strokemin 0 mm maximum spool stroke for a na-

    gative stroke

    SwitchingTimeOpen 3 ms time for opening motion

    SwitchingTimeClose 3 ms time for closing motion

    SwitchingThreshold 0 - Value of the input signal to open

    the valve

    CharacteristicEdgePA - - look-up table for the cross-

    section area of the valve

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    54 2008 FLUIDON GmbH

    Name Value Unit Description

    OverlapStrokePA 0 mm complete overlap for the meter-

    ing edge

    AlphaDPA 0.6 - flow coefficient for the edge

    from P to A

    TDifference 0 K Difference between local and

    system temperature

    Notes

    The component SWITCHINGVALVE22CHARACTERISTICS is a model of a 2-way switching valve. The flow characteristic is parameterized over a look-up table that defines the cross-section area in dependence of the stroke.

    For the look-up table, it is assumed that a positive Stroke opens the metering edge. The look-up table is displaced with the OverlapStroke of the metering edge to different start-ing points (see figure).

    It applies:

    OverlapStroke < 0: valve opened in resting position OverlapStroke = 0: valve just closed in resting position OverlapStroke > 0: valve closed in resting position

    cross-section-

    area

    0 Strokemax StrokenegativeOverlapStroke

    positiveOverlapStroke

    A1

    If the look-up table is defined in the range Stroke = 0..Strokemax the cross-section area does not exceed A1 in case of a negative overlap. If the look-up table is defined beyond Strokemax the cross-section area follows the look-up table.

    For Input > 0 the valve switches in positive direction up to Stroke = Strokemax, for Input 0 the valve switches in negative direction up to Stroke = Strokemin. The opening of the valve lasts always SwitchingTimeOpen, the closing always SwitchingTimeClose.

    The component SWITCHINGVALVE22CHARACTERISTICS does not represent a physical model of the valve but only its characteristic properties. Therefore the physical properties (e. g. mass of the spool, stiffness of the spring) are not parameterized.

    In addition, a model of this 2-way switching valve is also available as a component, at which the flow characteristic is determined by the parameters VolumeFlow and Pres-sureDifference (SWITCHINGVALVE22).

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    2008 FLUIDON GmbH 55

    ServoValve22P

    Symbol

    Sketch

    pP

    pAVolumeFlowPressureDifference

    Overlap

    Input

    1/InputMax

    StrokeVelocity

    Strokemin0Strokemax

    Connectors and Variables

    Name Type Unit Description

    pP Hydr bar supply pressure

    pA Hydr bar working pressure

    Input In - input signal for the spool stroke

    Stroke Out mm spool stroke

    VolumeFlow Out l/min volume flow

    Parameters

    Name Value Unit Description

    VolumeFlow 30 l/min flow through one metering edge

    at PressureDifference

    PressureDifference 35 bar see above

    Strokemax 1 mm maximum spool stroke for a

    positive stroke

    Strokemin 0 mm maximum spool stroke for a

    negative stroke

    InputMax 1 - standardization parameters for

    the input signal

    Overlap 0 % relative overlap of the metering

    edge

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    56 2008 FLUIDON GmbH

    Notes

    The component SERVOVALVE22P is a model of a 2-way proportional valve at which the stroke is proportional to the input signal. The flow characteristic is parameterized over the parameters VolumeFlow, PressureDifference and Overlap.

    The following rule is effective:

    Overlap < 0: valve opened in resting position Overlap = 0: valve just closed in resting position Overlap > 0: valve closed in resting position

    The component SERVOVALVE22P does not represent a physical model of the valve but only its characteristic properties. Therefore the physical properties (e. g. mass of the spool, stiffness of the spring) are not parameterized.

    In addition, a model of this 2-way proportional valve is also available as a component, at which the flow characteristic is parameterized with a look-up table (SER-VOVALVE22PCHARACTERISTICS).

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    ServoValve22PCharacteristics

    Symbol

    Sketch

    pP

    pA

    CharacteristicEdgePAOverlapStrokePA

    AlphaDPA

    Stroke

    Strokemin0Strokemax

    Input

    1/InputMax

    Connectors and Variables

    Name Type Unit Description

    pP Hydr bar supply pressure

    pA Hydr bar working pressure

    Input In - input signal for the spool stroke

    Stroke Out mm spool stroke

    VolumeFlow Out l/min volume flow

    Parameters

    Name Value Unit Description

    Strokemax 1 mm maximum spool stroke for a

    positive stroke

    Strokemin 0 mm maximum spool stroke for a

    negative stroke

    InputMax 1 - standardization parameters for

    the input signal

    CharacteristicEdgePA - - look-up table for the cross-

    section area of the valve

    OverlapStrokePA 0 mm complete overlap of the meter-

    ing edge

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    Name Value Unit Description

    AlphaDPA 0.6 - flow coefficient for the edge

    from P to A

    TDifference 0 K Difference between local and

    system temperature

    Notes

    The component SERVOVALVE22PCHARACTERISTICS is a model of a 2-way proportional valve at which the stroke is proportional to the input signal. The flow characteristic is parameter-ized over a look-up table that defines the cross-section area in dependence of the stroke.

    For the look-up table, it is assumed that a positive Stroke opens the metering edge. The look-up table is displaced with the OverlapStroke of the metering edge to different start-ing points (see figure).

    It applies:

    OverlapStroke < 0: valve opened in resting position OverlapStroke = 0: valve just closed in resting position OverlapStroke > 0: valve closed in resting position

    cross-section-

    area

    0 Strokemax StrokenegativeOverlapStroke

    positiveOverlapStroke

    A1

    If the look-up table is defined in the range Stroke = 0..Strokemax the cross-section area does not exceed A1 in case of a negative overlap. If the look-up table is defined beyond Strokemax the cross-section area follows the look-up table.

    The component SERVOVALVE22PCHARACTERISTICS does not represent a physical model of the valve but only its characteristic properties. Therefore the physical properties (e. g. mass of the spool, stiffness of the spring) are not parameterized.

    In addition, a model of this 2-way proportional valve is also available as a component, at which the flow characteristic is determined by the parameters VolumeFlow and Pres-sureDifference (SERVOVALVE22P).

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    2008 FLUIDON GmbH 59

    ServoValve22PT1

    Symbol

    Sketch

    pP

    pAVolumeFlowPressureDifference

    Overlap

    Input

    1/InputMaxTime constant

    StrokeStrokemin0Strokemax

    Connectors and Variables

    Name Type Unit Description

    pP Hydr bar supply pressure

    pA Hydr bar working pressure

    Input In - input signal for the spool stroke

    Stroke Out mm spool stroke

    VolumeFlow Out l/min volume flow

    Parameters

    Name Value Unit Description

    VolumeFlow 30 l/min flow through one metering edge

    at PressureDifference

    PressureDifference 35 bar see above

    T 50 ms time constant true for:

    xE n < xE n+1

    TDecreasing 0 ms time constant true for:

    xE n > xE n+1

    Strokemax 1 mm maximum spool stroke for a

    positive stroke

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    60 2008 FLUID